This invention relates to a method of synchrotron acceleration and a circular accelerator and more particularly to the acceleration method and accelerator suitable for stably accelerating a high current or a great number of charged particles to obtain a high current at high energy in industrial radiation sources.
The industrial radiation source is required to be a small-scale source which can be installed in, for example, a semiconductor factory and which can generate radiation of high brightness (high current) in order to decrease the irradiation time. A known way to meet the above requirement is to inject charged particles at low energy into the circular accelerator and synchrotron accelerate the charged particles.
In synchrotron acceleration of charged particles, a beam current injected into the RF acceleration cavity creates a reactance component due to beam loading in the cavity during acceleration of the injected charged particles from low energy to high energy. This reactance component causes the resonance frequency of the RF acceleration cavity to deviate from the oscillation frequency of the RF oscillator. If the frequency offset is left as it is, there results a failure to apply a predetermined acceleration voltage to the charged particles. The offset between the oscillation frequency and resonance frequency is called a modulated frequency component or a detuned amount. A processing for correcting the modulated frequency or detuned amount is called herein frequency modulation or detuning.
In a conventional method of synchrotron acceleration of charged particles as disclosed in "Characteristics of RF Acceleration Cavity", INS-TH-96, Institute for Nuclear Study, University of Tokyo, Feb. 18, 1975, RF power to be supplied to the RF acceleration cavity is controlled while making the detuned amount constant at all times from beginning to end of acceleration so as to apply a constant acceleration voltage to the charged particles all the time.
This prior art synchrotron acceleration method is represented at X in FIG. 2 where ordinate represents RF power and abscissa the detuned amount. In the graphic representation of FIG. 2, the RF power is related to the detuned amount by curves I, I and III with the energy level of the charged particles is increased in order of curves I, II and III. Thus, curve I is representative of the initial energy state of the charged particles, curve II is representative of the intermediate energy state and curve III is representative of the ultimately reached energy state.
As indicated at X in FIG. 2, in the prior art acceleration method on synchrotron acceleration basis, the detuned amount is fixed and only the RF power is controlled.
However, when only the Rf power is controlled with the detuned amount fixed during the injection of charged particles as in the case of the prior art method, there arise problems which will be described hereinafter. Here, however, the relation between the detuned amount and RF power will be first explained.
Where f is the oscillation frequency of RF oscillator and f.sub.o is the resonance frequency of RF acceleration cavity, the detuned amount, .DELTA.f, is defined as EQU .DELTA.f.ident.f-f.sub.o
and this formula is reduced to EQU .DELTA.f=1/2Q.sub.o .multidot.I.sub.o R.sub.s /V.sub.c .multidot.sin.PHI.s.multidot.f
where
Q.sub.o : unloaded Q of the RF acceleration cavity, PA1 I.sub.o : beam current, PA1 R.sub.s : Shunt impedance of the acceleration cavity, PA1 V.sub.c : acceleration cavity voltage, and PA1 .PHI.s: acceleration phase.
Under this condition, the RF power Pg, necessary for accelerating charged particles corresponding to the beam current I.sub.o is given by EQU Pg=V.sub.c.sup.2 /R.sub.s .multidot.(1+.beta.).sup.2 /4.beta..multidot.[tan.sup.2 .PSI.+2sin.PHI.s tan.PSI.+1+.alpha..sup.2 +2.alpha.cos.PSI.s]
where tan .PSI.=2Q.sub.o /(1+.beta.).multidot..DELTA.f/f, .alpha.=I.sub.o R.sub.s /V.sub.c (1+.beta.) and .beta.is a coupling constant with an external circuit.
Gathering from .DELTA.f and Pg determined as above, it will be appreciated that the detuned amount tends to increase as the beam current I.sub.o increases and acceleration cavity voltage V.sub.c decreases while the RF power tends to increase as the acceleration cavity voltage V.sub.c increases.
Accordingly, if the acceleration cavity voltage V.sub.c is low at the initial injection of the charged particles having low energy, the detuned amount will become large. Then, if only RF power is controlled with the detuned amount fixed at a large value, the RF power will be supplied insufficiently to the charged particles at the final stage of acceleration when the acceleration cavity voltage is high so that a desired amount of current can not be obtained. This conventional acceleration procedure is indicated at Z in FIG. 2.
Conversely, if the detuned amount is fixed initially at a small value which would appear near the final stage of acceleration when the acceleration cavity voltage V.sub.c is high, the synchrotron oscillation deviates from a stable range at low energy region, falling in an unstable phase range as indicated at dotted-line portion of curve I or II in FIG. 2, resulting in beam loss. This conventional acceleration procedure is indicated at X in FIG. 2. In the unstable phase range, the beam current I.sub.o can not be maintained and is forced to decrease. It is therefore clear that the above conventional acceleration procedures are unsuited for accelerating charged particles to obtain the high current at high energy.
Disadvantageously, the prior art synchrotron acceleration method has problems in that the charged particles can not therefore be accelerated to produce a high current at high energy without beam loss and industrial small-scale, high-brightness radiation sources can not be obtained.